President Barack Obama said Monday that he would detail his administration’s proposals to prevent gun violence later this week, even as his former chief of staff provided him with some unsolicited advice about how to push gun control legislation through a bitterly divided Congress.

Obama told reporters at a news conference that he would announce his proposals by the end of the week after reviewing a set of policy recommendations issued by Vice President Joseph R. Biden Jr.’s task force on gun violence.

“I expect to have a fuller presentation later in the week to give people some specifics about what I think we need to do,” Obama said one month to the day after a gunman killed 26 people, including 20 first-graders, at an elementary school in Newtown, Conn. “My starting point is not to worry about the politics. My starting point is to focus on what makes sense, what works, what should we be doing to make sure that our children are safe and that we’re reducing the incidents of gun violence.”

While emphasizing that he would review Biden’s recommendations before announcing his legislative plans, Obama reiterated his support for at least three ideas he has backed previously: stronger background checks on those who purchase firearms; a prohibition on high-capacity ammunition magazines; and a reinstatement of the federal assault weapons ban that expired in 2004. He suggested that those three components will be part of his proposal.

“Those are things I continue to believe make sense,” Obama said. “Will all of them get through this Congress? I don’t know. But what’s uppermost in my mind is making sure that I’m honest with the American people and with members of Congress about what I think will work.”

Separately Monday, a key Senate Democrat said lawmakers and the White House are evaluating how broad any legislative gun control package should be.

“I think that Vice President Biden, as well as those of us in the Senate who have been involved in the pro-gun-safety movement, and those in the House, are trying to figure out the maximum package that we think is passable,” Sen. Charles E. Schumer, D-N.Y., told reporters.

Although Obama and Schumer provided few new details about the scope of the proposals, the president’s former chief of staff, Chicago Mayor Rahm Emanuel, said there are ways the administration can improve its chances of passing legislation this year.

Emanuel — who served in Congress from 2003 to 2009, including a stint as House Democratic Caucus chairman — helped secure passage of major gun control legislation as a senior adviser to President Bill Clinton in 1994. He said the White House should fine-tune its political message to frame the policy debate on its terms; kick off its legislative push in the Senate rather than the House; and use executive powers to make some changes administratively while prodding lawmakers into broader action.

“Focus the argument on the criminals’ access [to guns] and you’re going to get a bipartisan majority,” Emanuel said during a panel discussion at the Center for American Progress, a liberal think tank with ties to the administration. “It’s not about ‘gun control.’ It’s about ‘criminal access to guns.’ That changes the debate.”

Emanuel said the administration can build support on Capitol Hill if it enlists law enforcement officers as advocates and focuses its messaging on the most dangerous kinds of guns and high-capacity ammunition magazines.

The legislative process, he advised, must start in the Democrat-led Senate. If the Senate passes a gun law overhaul, he said, the Republican-led House would face intense political pressure to take up the measure. “Whatever you do, start in the Senate,” he said.

Emanuel also suggested that Obama use his executive authority not only to make policy changes administratively but also as a bargaining chip to persuade Congress to pass legislation that makes more-sweeping changes.

“Congress never likes the president doing something that they think they have the authority for,” Emanuel said, noting that one possible step would be for the president to ask the Justice Department to place more emphasis on the prosecution of gun crimes. “So if you want to spur [lawmakers], start taking some of the real estate. It will get them moving quicker.”

Obama said Monday that executive orders are on the table, and he provided a hint about the White House’s messaging in the weeks ahead by discounting gun rights groups’ claims that he intends to infringe on Americans’ Second Amendment rights.

“If you look over the first four years of my administration, we’ve tried to tighten up and enforce some of the laws that were already on the books,” Obama said. “But it’d be pretty hard to argue that somehow gun owners have had their rights infringed.”